Canonical quantization of relativistic balls of dust

The Hamiltonian form for the equations of a relativistic perfect fluid is considered and later specialized to the case of spherical symmetry and vanishing pressure. When comoving coordinates are used in the canonical formalism, one gets a reduced Hamiltonian which is independent of time. The continuous number of degrees of freedom are decoupled and the Schr\"odinger equation separates from a functional differential equation to a set of identical ordinary differential equations. Boundary conditions for these equations are naturally obtained by requiring that the minisuperspace be geodesically complete. The formalism remains the same whether one treats a closed nonhomogeneous universe or a collapsing star. The problem of singularities is discussed, and it is concluded that in this minisuperspace quantum formalism there is no inevitable singularity.